Because [tex] \pi [/tex] is defined as the ratio between the circumference and the radius.
This ratio happens to remain constant in every circle: no matter how big or small you make it: the circumference will always be a multiple of the radius, and the constant of proportionality is always be [tex] \pi [/tex]
Of course difference circles will have different circumference, but [tex] \pi [/tex] doesn't depend on the circumference because, when you divide it by the radius, the result will always be the same.
A similar example is the fact that the square of a diagonal is always [tex] \sqrt{2}s [/tex], if s is the side length. No matter how big or small the side is, the diagonal will always be [tex] \sqrt{2} [/tex] times the side.
It's the constant of proprtionality that matters, not the specific values involved in the proportion!
